Blue Heaven 2s or LAT International SS-1000 Mk IIs

A direct comparison would be the only way, as Hassel states above. The Blue Heaven is well-known and highly regarded by many users and reviewers and it would be worth your while to check it out. I have BH and think it is superb for the $$. I don't know about the LAT

But, TRY THIS for truly amazing sound (if you want to spring for the money). For SOUND EQUIVALENT TO NORDOST SPM ($3,800 list for a 3m pair), try TWO RUNS of Nordost Blue Heaven Rev II , i.e. a double bi-wire set. For $650-$700 used (total) you have amazing cables. Some have known about this and I recently asked Nordost and they agreed that, yes, it is "equivalent" to SPM, though the two would sound slightly different. SPM was Nordost's top of the line until Valhalla and to get the equivalent from BH is truly amazing at such a low price.

I use the two runs of BH and feel I have a top set of cables and have no further need to upgrade or spend big bucks on e.g., SPM. I don't expect to go for Valhalla.

I do not think the Blue Heaven would be a serious competition fo the LAT. I compared Nordost´s more expensive Red Dawn to the SS 1000 in its first version, and it did not sound better. The SS 1000 Mk II, which I upgraded too is even better. So my advise would be to order the LAT first, burn it in for the larger part of the 45 days recommended, and doing a home-comparison with a Nordost from your local dealer or from the Cable Company.